Abstract

We present and analyze a second order in time variable step BDF2 numerical scheme for the Cahn-Hilliard equation. the construction relies on a second order backward difference, convex-splitting technique and viscous regularizing at the discrete level. We show that the scheme is unconditionally stable and uniquely solvable. in addition, under mild restriction on the ratio of adjacent time-steps, an optimal second order in time convergence rate is established. the proof involves a novel generalized discrete Gronwall-type inequality. as far as we know, this is the first rigorous proof of second order convergence for a variable step BDF2 scheme, even in the linear case, without severe restriction on the ratio of adjacent time-steps. Results of our numerical experiments corroborate our theoretical analysis.

Department(s)

Mathematics and Statistics

Comments

National Natural Science Foundation of China, Grant 11331004

Keywords and Phrases

Cahn-Hilliard Equation; Convergence Analysis; Variable Step BDF2 Scheme

International Standard Serial Number (ISSN)

0036-1429

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2023 Society for Industrial and Applied Mathematics, All rights reserved.

Publication Date

01 Jan 2019

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